Numerical 2D modelling of turbulent melt flow in CZ system with dynamic magnetic fields

摘要

The paper presents results of 2D axisymmetric mathematical modelling of laboratory CZ model facility that corresponds well to a large industrial silicon CZ growth system. The purpose of the investigation is to examine turbulent melt flow features that develop in the model crucible, when various dynamic magnetic fields (travelling, alternating) are applied, and to test the applicability of the modified low Re k-ε turbulence model for the calculation of flows in these cases by extensive comparisons between calculated and measured data. The electromagnetic field is calculated with a self-developed program, and the calculations of the melt motion are carried out with the user modified hydrodynamic program package CFD-ACE. Extremely fine grid and the modified low Re k-ε turbulence model are used in hydrodynamic calculations. The flow features and temperature fields are investigated, and the influence of dynamic field strength and crucible and crystal rotation is shown. A comparison between calculation results and temperature measurements in a corresponding laboratory model with low-temperature InGaSn eutectic has shown good agreement.